1. Field of the Invention
This invention relates to radar signal processing. In particular, this invention concerns signal processing of agile Pulse Repetition Time (PRT) sampled signal transmitted using spread spectrum technique.
2. Discussion of the Background
Radio frequency (RF) pulse-to-pulse agility is a frequency hopping known as a spread spectrum technique. By RF pulse-to-pulse agility involves changing the carrier frequency per pulse. This implies a much wider frequency band than the minimum bandwidth required to transmit and receive a pulse.
The main advantage of RF pulse-to-pulse agility is the increase of the resistance against jamming and interference. The spread spectrum has been improving radar and communication since the forties and eighties respectively. Besides the jamming suppression, such spread spectrum can also result in a high range resolution, frequency correlation . . .
Even when the corresponding Doppler velocity remains constant within a burst (i.e. within coherent processing interval), such RF pulse-to-pulse agility implies time-varying Doppler spectra. The spectral analysis of time varying spectra means in radar application Doppler processing when Doppler frequency changes from one pulse to another.
Conventional Doppler processing can not suffice as it is based on constant frequency during a burst. This is the reason why the combination of the RF agility with coherent processing has always been considered difficult if not impossible.
Even when radar signals with the Doppler phase could be extracted per pulse, major problems would just begin in Doppler processing, mainly because the received Doppler phase as well as the target radar cross section could differ for different carriers.
In a fully coherent radar, all frequencies are generated from one single reference oscillator, so the phase coherence is inherent. Carrier frequency fRF, intermediate frequencies fA and fLO, sampling frequency fS and pulse repetition frequency fPRF are generated from one and only oscillator. In addition, RF agile radar requires more than one intermediate frequency fA,n so that a number of different frequency per pulse fRF,n can be generated.
Coherent integration necessitates non-random phases of reflected pulses. In a coherent radar, the transmitted phase is known, but such a well-controlled phase may be damaged during the propagation.
At time delay t after the nth pulse, the received radar signal s(tn), tn=τ+(n+1)tPRT (after analogue-digital conversion), can be modelled as follows:s(tn)=α·g(ωtn−θ)·ejφ(tn)ejφ(tn)where α, g( ) and φ( ) represent the complex target echo depending on the target radar cross section, the two-way antenna voltage gain pattern with the scan rate ω and the target azimuth θ, and the instantaneous phase, respectively. The antenna pattern is assumed to be constant within a burst, e.g. g( )=1. In general, the pulse repetition time tPRT will also be constant.
Another drawback of the RF agility is that the RF agility can make the target echo α fluctuate independently from pulse to pulse, if a target contains many scatterers instead of one single scatterer and, moreover, if the individual scatterers move randomly.
If one (dominant) scatterer and no pulse-to-pulse dependence are assumed, the phases of reflected pulses remain non-random. Other Doppler processing than discrete Fourier transform is needed, unless samples are gathered from the pulses with the same frequency.
In an extreme target model such as e.g. the Swerling model II, many scatterers contribute equally to the echo signal. The resulting amplitude is Rayleigh distributed and the resulting phase can only be assumed to be uniformly distributed in [0, 2π]. Accordingly, no Doppler processing but incoherent integration only is applicable.
By assuming reflectors not interacting or moving randomly, there are non-random phases needed. However, the amplitude variability is significantly less troublesome than the variability of the phase. In general, it would add noise in results of the Doppler processing.
Decorrelation of radar echoes implies no coherence, i.e. no knowledge of the phases or, finally, of radial velocities. Fortunately, there are islands of frequency correlation that depend on the target dimensions and position but also on radio frequency and its change. Thus, the RF agility pattern can be chosen that result in correlated radar echoes what enable coherent processing.
In any case, time-varying spectra are present in a coherent Doppler RF agile pulse radar. Thus, the Fourier analysis does not apply anymore.
In the article “High Accuracy 35 GHz Tracking Radar”, Oderland, I., Nordlöf, Leijon, B., Proceedings of IEEE International Radar Conference 1990, time-varying spectra were avoided by combining pulses with the same carrier. This article discloses that such method can be applied only with constant pulse repetition time (PRT). However, this waveform lowers Doppler range. This means that the range of possible unambiguous Doppler velocities decreases fast with increasing number of different carrier frequencies in a burst.